Syllabus:
This is a standard introduction to the theory of analytic functions of
one complex variable.
The main topics are contour integration, Cauchy's Theorem,
power series and Laurent series expansions of analytic functions,
classification of isolated singularities,
and the residue theorem with its applications
to evaluation of definite integrals.
If time permits, we will also discuss
the argument principle and Rouché's Theorem,
analytic continuation, harmonic functions,
and conformal mapping (including fractional linear transformations).

Recommended Reading: The Sarason text is concise and without many figures or worked examples, so you are encouraged to look also at at least one other text, such as one of the following:

Marsden and Hoffman, Basic complex analysis, 3rd edition, W. H. Freeman, 1998. (I used this book the last time I taught Math 185, but decided against it this time, since it now costs $153, nine times as much as Sarason's book!)

Grading: 35% homework, 15% first midterm, 15% second midterm, 35% final.
Each homework grade below the weighted average
of your final and midterm grades will be boosted up to that average.
The course grade will be curved.
Click here for an example.

Homework: There will be weekly assignments due at the
beginning of class each Wednesday.
Late homework will not be accepted, but see the grading policy above.
You should not expect to be able to solve every single problem on your own;
instead you are encouraged to discuss questions with each other
or to come to office hours for help.
If you meet with a study group,
please think about the problems in advance
and try to do as many as you can on your own before meeting.
After discussion with others, write-ups must be done separately.
(In practice, this means that you should not be looking
at other students' solutions as you write your own.)
Write in complete sentences whenever reasonable.
Staple loose sheets!